Units in HYDRUS

Basic Units:

Length Units: [Ls], [Lw] = meters, centimeters, millimeters.

Time units: [T] = seconds, minutes, hours, days, years.

Mass Units: [Mc] – mass of solute, [[Mc] = mg, g, mol, meq, etc; Ms] – mass of soil; [Ms] = g, mg, kg, etc

Units for concentration, c, in Hydrus are mass of solute [Mc] per volume [Lw3] of water, i.e., [Mc/Lw3], i.e., solute concentration in the liquid phase. In general, concentration units should be consistent with the length units [L] being used in the rest of the project.

Derived Units:

The derived units for 1D problems are now as follows:

Transport domain, A: 1D: [Ls], 2D: [Ls2], 3D: [Ls3]

Boundary Length, L: 1D: [-], 2D: [Ls], 3D: [Ls2]

Water content, θ: [Lw3/Ls3], i.e., volume of water per volume of soil.

Concentration, c: [Mc/Lw3]

Sorbed concentration, s: [Mc/Ms], i.e., mass of solute per mass of soil.

Total concentration, S=θc+ρs: [Mc/Lw3] [Lw3/Ls3] + [Ms/Ls3] [Mc/Ms]= [Mc/Ls3]

Amount of solute in the soil domain, (θc+ρs)A=SA:

1D: [Mc/Lw3] [Lw3/ Ls3]*[Ls]= [Mc/Ls2]

2D: [Mc/Lw3] [Lw3/ Ls3]*[Ls2]= [Mc/Ls]

3D: [Mc/Lw3] [Lw3/ Ls3]*[Ls3]= [Mc]

Water flux, q: [Ls/T]

Solute flux, qc: [Mc/Lw3*Ls/T] = (when Lw=Ls) = [Mc/Lw2/T]

Cumulative solute flux, qcLt:

1D: [Mc/Lw2/T][-][T]=[Mc/Lw2]

2D: [Mc/Lw2/T][Ls][T]=[Mc/LW]

3D: [Mc/Lw2/T][Ls2][T]=[Mc]

Cumulative zero-order reaction, γθtA

1D: [Mc/Lw3/T] [Lw3/ Ls3] [T]*[Ls]= [Mc/Ls2]

2D: [Mc/Lw3/T] [Lw3/ Ls3] [T]*[Ls2]= [Mc/Ls]

3D: [Mc/Lw3/T] [Lw3/ Ls3] [T]*[Ls3]= [Mc]

Cumulative first-order reaction, μθctA

1D: [1/T] [Lw3/ Ls3] [Mc/Lw3] [T]*[Ls]= [Mc/Ls2]

2D: [1/T] [Lw3/ Ls3] [Mc/Lw3] [T]*[Ls2]= [Mc/Ls]

3D: [1/T] [Lw3/ Ls3] [Mc/Lw3] [T]*[Ls3]= [Mc]

Inspection of the governing advection-dispersion equation shows that the concentration variable appears in most or all terms (except certain production and reaction terms). Consequently, the concentration [Mc/Lw3] does not necessarily have to be given in the same length units [Lw], as the transport domain [Ls]. However, one then needs to convert variables derived from concentrations (given above) to account for this mismatch of units (between concentration and length units).

Conversions of Heat Transport Parameters (Why the large numbers for some variables and some units?)

Although the apparent (derived) units for the thermal conductivity and the thermal capacity are (W/m/K) and (J/m3/K), respectively, the basic SI units (i.e., in mass, length, and time) are [ML/T3/K] and [M/L/T2/K], respectively. Thus when converting the thermal conductivity or the thermal capacity to new time units, one needs to make conversions directly in the basic SI units, and to convert time to the third or second power, respectively. The same is true for the length units. Note that when one converts the HYDRUS project to meters and seconds, one will get the familiar values of the thermal capacity and thermal conductivity.